An Adaptation for Iterative Structured Matrix Completion

Matrix completion is the task of predicting missing entries of matrix from a subset of known entries. Notions of structured matrix completion include any setting in which whether an entry is observed does not occur uniformly at random. In recent work, a modification to the standard nuclear norm minimization for matrix completion has been made to take into account sparsity-based structure in the missing entries, which is motivated e.g. in recommender systems. In this work, we propose adjusting an Iteratively Reweighted Least Squares (IRLS) algorithm for low-rank matrix completion to take into account sparsity-based structure. We also outline an iterative gradient-projection-based implementation of the algorithm that can handle large-scale matrices. Lastly, we present preliminary numerical experiments showcasing the performance of the proposed method compared to the standard IRLS algorithm in structured settings.